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研究生: 吳韋志
Wu, Wei-Chih
論文名稱: 背向階梯下游流場發展之實驗分析
Experimental Research on the Downstream Development of the Backward-facing Step Flow
指導教授: 張克勤
Chang, Keh-Chin
王覺寬
Wang, Muh-Rong
學位類別: 碩士
Master
系所名稱: 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年: 2009
畢業學年度: 97
語文別: 中文
論文頁數: 89
中文關鍵詞: 偏態係數再成長邊界層背向階梯峰態係數
外文關鍵詞: skewness, kurtosis, redeveloped boundary layer, backward-facing step
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  • 本文主要是以背向階梯流場中的下游發展現象與演化過程作為研究目標,探討一階梯高為10mm,其突張比為1.13的標準背向階梯結構中,固定入口自由流平均速度為15.09m/s,藉由以不同的初始進口條件改變實驗的控制參數Reθ,來觀察其對下游流場的發展現象之影響。
    本研究係以Reθ為878及1053兩不同的初始進口條件,以紊流強度及雷諾剪應力來觀察下游流場的邊界層與自由流間的分布外,也加入了三階紊流參數(Turbulent triple-product)來探討階梯下游流場的相關紊流特性,同時也比較了下游流場不同截面的偏態係數(Skewness)與峰態係數(Kurtosis)的分布。而由實驗結果得知,在背向階梯下游流場的發展現象中,不論是代表速度擾動值的紊流強度或是動量傳遞大小的雷諾應力,其演化的過程均是隨著流場往下游的發展而呈現消退且擴散的趨勢,係符合了紊流能量傳遞的瀑流原理(energy cascade theory)。
    此外,由於邊界層內的流體動量均是往自由流區傳遞,故在自由流與邊界層的交界面有著間歇性的渦流傳遞現象存在,而此交界處產生的間歇性渦流流逸(intermittent bursts)便造成了速度分布的偏斜現象,而偏態及峰態係數在統計學上便是用來分析資料偏斜與離散程度的因子,在相較於以平均速度分布來判定邊界層厚度而言,此間歇性的渦流流逸其所能造成平均值上的影響是有限的,故以偏態係數及峰態係數來判定再成長邊界層的分布,則是較符合流體現象上的物理意義。而由實驗結果觀察到,Reθ值的大小對於背向階梯下游流場之再成長邊界層的發展過程則是有顯著的影響。

    The purpose of this thesis is to experimentally explore the downstream development of backward-facing step flow with the configuration of 10 mm in step’s height and 1.13 in the aspect ratio under two different Reynolds numbers of Reθ = 878 and 1053.
    The inlet mean velocity is fixed at 15.09 m/s but the inlet Reynolds numbers based on the momentum boundary thickness, Reθ, are changed by means of controlling the inlet momentum boundary layer thickness .
    Evolution of the sectional files of turbulent proportions including turbulent intensities, Reynolds stress, some turbulent triple-products, skewness coefficient and kurtosis coefficient are presented under the two different conditions of Reθ = 878 and 1053. It is found that the turbulent intensities and Reynolds stress are decayed and diffused from the boundary layer to the free stream region along the flow direction. The evolution tendency is consistent with the turbulent energy cascade theory.
    There exist the intermittent burst in the interface between the boundary layer and the free stream region, which leads to the skewness of the instantaneous velocity distributions. It is more physically meaningful in estimating the redeveloped boundary layer thickness on the bases of the peak values of the skewness coefficient and the kurtosis coefficient than on the basis of the mean streamwise velocity distribution. It is found that the Reθ value has significant effect on the development of the redeveloped boundary layer.

    摘要 I Abstract III 誌謝 V 目錄 VI 表目錄 VIII 圖目錄 IX 符號說明 XIII 第一章 緒論 1 1.1 前言 1 1.2 文獻回顧 2 1.2.1 基本背向階梯流場 2 1.2.2 背向階梯流場之暫態分析 6 1.2.3 背向階梯流場之相關研究 8 1.3 研究目標 10 第二章 實驗設備與模型 12 2.1 實驗設備 12 2.1.1 供氣系統 12 2.1.2 風洞設備 12 2.1.3 三維移動平台 14 2.1.4 量測系統 14 2.1.4-1 水柱式微壓計 14 2.1.4-2 壓力轉換計 15 2.1.4-3 熱線測速儀 15 2.1.5 資料擷取系統 17 2.1.5-1 NI-DAQ資料擷取系統 17 2.2 實驗模型 17 2.2.1 背向階梯模型 18 2.2.2 座標定義 18 第三章 實驗方法與分析 19 3.1 實驗方法 19 3.1.1 實驗規劃與流程 19 3.1.2 量測誤差估計 20 3.2 參數分析 21 3.2.1 邊界層動量厚度 ( Momentum thickness ) 21 3.2.2 雷諾數 ( Reynolds number ) 22 3.2.3 再成長邊界層之紊流特性分析 22 3.2.3-1 紊流強度 ( Turbulence intensity, T.I. ) 22 3.2.3-2 雷諾剪應力 ( Reynolds stress, Rij ) 23 3.2.3-3 三階紊流參數 ( Turbulent triple-product ) 24 3.2.3-4 偏態係數 ( Skewness ) 25 3.2.3-5 峰態係數 ( Kurtosis ) 26 3.2.3-6 快速傅立葉轉換 ( Fast-Fourier-Transform , FFT ) 27 第四章 結果與討論 28 4.1 流場特性 28 4.2 再成長邊界層之紊流特性分析 33 4.2.1 紊流強度 ( Turbulence intensity ) 33 4.2.2 雷諾應力 ( Reynolds stress ) 35 4.2.3 三階紊流參數 ( Turbulent triple-product ) 36 4.2.4 偏態係數 ( Skewness ) 38 4.2.5 峰態係數 ( Kurtosis ) 40 4.2.6 邊界層動量、位移厚度 41 4.3 綜合討論 41 第五章 結論與建議 43 5.1 結論 43 5.2 未來建議 43 參考文獻 45

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